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Strengthened SHS Curriculum - General Mathematics-Sequences & Series.pptx

Strengthened SHS Curriculum - General Mathematics Lesson 3

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25, 50, 75, 100, 125, ... 4, 5, 6, ... 4, 7, 10, 13, 16, ... 3, 5, 6 4, 7, 1 16, 2, 10, 50, 250, 1250 ... -2, 10, -50, 250, - , 10, 50, 250, 1250 ... 9, 18, 27, 36, 45, .... -6, -8, -10, -12, - 14, ... 10, 20, 30, 40, 50 10, 20, 30, 40, 50, ... 3, 5, 6, 7, 8, ... 4, 7, 10, 13, 16, ... 7, 21, 63, 189, 567 11, 22, 33, 44, 55, ... 9, 18, 8, 16, 32,... 1 3 , 1 6 , . . . 7, 21, 63, 189, 567, .... , 5, 6, ... 4, 7, 10, 13, 16, ... 6, 32,... 3, 5, 6, 7, 13, 16, 2, 10, 50, 3, 5, 6, 7, 2, 5, 6, ... 2, 10, 50, 250, 1250 3, 5, 6, 7, 8, ... 4 , 7 , 1 0 , 1 3 , 1 6 , . . . -2, 10, -50, 250, - 1250 ... 10, 20, 30, 40, 50, ... 7, 21, 63, 189, 567, ... 2, 3, 4, 5, 6, ... Sequences & Series
Activity – Spin the Wheel of Names Spin the wheel with the students’ names on it. Let the picked students answer the given question on the board.
Activity – Spin the Wheel of Names 1) 2, 4, 6, _ • Give the next missing term. • Give the rule.
Activity – Spin the Wheel of Names 2) 1, 1, 2, 3, _ • Give the next missing term. • Give the rule.
Activity – Spin the Wheel of Names 3) 100, 90, 80, _ • Give the next missing term. • Give the rule.
Activity – Spin the Wheel of Names 4) Square tile patterns: 1 tile, 4 tiles, 9 tiles, _ • Give the next missing term. • Give the rule.
Activity – Spin the Wheel of Names 5) 3, 6, 9, 12, _ • Give the next missing term. • Give the rule. • 3 + 6 + 9 + 12 + 15 = _
Activity – Spin the Wheel of Names 6) 0.1, 0.2, 0.3, _ • Give the next missing term. • Give the rule. • 0.1 + 0.2 + 0.3 + 0.4 =
Key Terms and Definitions Series - the sum of the terms of a sequence. Example: For the sequence 1, 3, 5, the series is 1 + 3 + 5 = 9
Key Terms and Definitions Finite Series - a series with a definite number of terms. Example: 2 + 4 + 6 + 8 (only 4 terms)
Key Terms and Definitions Infinite Series - a series that continues without end. Example: 1 + ½ + ¼ + 1/8 + …
Key Terms and Definitions The nth term of a sequence is usually denoted by an Partial Sum (Sn) - the sum of the first (n)
Key Terms and Definitions If the nth term of the sequence is an, then Sn = a1+a2+a3+...+an Example: In the sequence, 1, 3, 5, 7, 9, ..., S4 = 1 + 3 + 5 + 7 = 16 Sn is the nth term of the series
Key Terms and Definitions Sigma Notation ( ) - a shorthand ∑ symbol used to express a series. To write a1 + a2 + a3 + … + an in sigma notation:
Key Terms and Definitions In general, (expression in terms of an) Example: 1 + 2 + 3 + 4 + 5 in sigma notation is
Let’s Practice (Saving Up Smartly – A Real- Life Application of Sequences) Scenario: A student wants to build a personal savings fund. They commit to saving ₱50.00 in the first week and increase the amount they save by ₱15.00 each week. Week 1: ₱50.00 Week 2: ₱65.00 Week 3: ₱80.00
Let’s Practice (Saving Up Smartly – A Real- Life Application of Sequences) Question: 1) How much will the student save in Week 10? 2) How much will the student have saved in total after 10 weeks?
Let’s Practice (Saving Up Smartly – A Real- Life Application of Sequences) Question: 3) If the student’s goal is to save ₱1,500.00, in how many weeks will the goal be met or exceeded? 4) How can this type of savings plan help in achieving financial goals such as buying a gadget, funding a project, or starting a small business?
Evaluating Learning 1) Which of the following best describes a series? A) A sum of numbers in a pattern B) A list of numbers in a specific order C) A variable expression with a pattern D) A formula for a term
Evaluating Learning 2) Which of the following is a series? A) 2, 4, 6, 8 B) 3, 6, 9, 12 C) 2 + 4 + 6 + 8 D) 1, 3, 5, 7
Evaluating Learning 3) What does the sigma symbol ( ) represent in ∑ mathematics? A) A product B) A term C) A square root
Evaluating Learning 4) What is the sigma notation of the series 5 + 10 + 15 + 20? A) C) B) D)
Evaluating Learning 5) What is the sigma notation for 1 + 3 + 9 + 27? A) C) B) D)
Answers Key 1) A 2) C 3) D 4) A 5) B